Application of weighted-residual methods to investigate the nonlinear dynamics of boiling water reactors

This dissertation describes the application of weighted-residual methods to investigate the nonlinear dynamics of boiling water reactors (BWRs). Under proper conditions, BWRs can become linearly unstable and experience steady-state limit-cycle oscillations. Weighted-residual methods were used to obtain approximate solutions describing overall BWR dynamic behavior during these oscillations.

Two BWR dynamic models were used in this investigation. The first model qualitatively describes the reactor dynamics and is useful for examining the effect of various reactor parameters on the limit cycle. The second model uses the more accurate thermal hydraulics model contained in the BWR stability code LAPUR, allowing this model to quantitatively describe the behavior of specific reactors during low-amplitude, steady-state, limit-cycle oscillations. Both dynamic models use the point kinetics equations to describe the neutronics.

High- and low-order approximate solutions describing steady-state limit-cycle oscillations of the overall weighted neutron population were obtained by applying Galerkin's method. The approximate solutions were in the form of Fourier series and can describe either regional or core wide oscillation modes. The approximate solutions were found to converge to the exact solution as more harmonics were included in the approximation. The low-order approximate solutions were used to examine BWR dynamic behavior near the stability boundary, to develop stability conditions for both BWR dynamic models, and to examine the effect of model parameters (and therefore the related reactor parameters) on reactor stability. Bifurcations of the limit cycle were also investigated. Equations describing the dynamic behavior of perturbations about a candidate limit cycle of the unbifurcated form were derived. Bifurcation tests based on the asymptotic stability of these perturbations were developed by applying both weighted-residual methods and Floquet’s theory. If the candidate limit cycle was unstable, numerical results showed that the perturbations established their own limit cycle. An approximate solution for this limit cycle was obtained by applying Galerkin's method. Adding the approximate solution describing the limit cycle of the perturbations to the unbifurcated candidate limit cycle gave an approximate solution for the bifurcated limit cycle.